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arXiv:2606.05060

High-fidelity neutral atom gates leveraging low-rank Hessian optimization

Genyue Liu, Guillaume Bornet, Deniz Kurdak, Mingxuan Xiao, Chenyuan Li, Bichen Zhang, Jeff D. Thompson

quant-phphysics.atom-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
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Abstract

Quantum optimal control can produce fast and robust multi-qubit gates, but experimentally calibrating the resulting high-dimensional waveforms remains challenging because direct searches over large parameter spaces converge slowly. Building on the low-rank structure of quantum-control landscapes, we develop and benchmark a Hessian-based calibration method for optimal-control gates. The method identifies the few waveform directions that affect fidelity to leading order, with the number of directions set by the accessible leakage and coherent error channels, and optimizes only within this principal space using closed-loop experimental feedback. We apply this approach to an amplitude-robust controlled-Z gate on metastable-state 171Yb nuclear-spin qubits. Experimentally, we verify the predicted Hessian-sensitive directions and demonstrate rapid convergence of the optimization protocol. The optimized gate reaches a raw fidelity of 0.9959(2), increasing to 0.99902(7) after postselection on no detected loss, and the performance is essentially unchanged under laser-power variations of up to 20%. We further show that the same fidelity Hessian directions can correct certain Hamiltonian parameter errors. These results establish low-rank Hessian optimization as an efficient and physically motivated calibration strategy for high-dimensional optimal-control gates, which is broadly applicable to many qubit types.

Comments
16 pages, 10 figures, 1 table

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Quantum optimal control can produce fast and robust multi-qubit gates, but experimentally calibrating the resulting high-dimensional waveforms remains challenging because direct searches over large parameter spaces converge slowly. Building on the low-rank structure of quantum-control landscapes, we develop and benchmark a Hessian-based calibration method for optimal-control gates. The method identifies the few waveform directions that affect fidelity to leading order, with the number of directions set by the accessible leakage and coherent error channels, and optimizes only within this principal space using closed-loop experimental feedback. We apply this approach to an amplitude-robust controlled-Z gate on metastable-state 171Yb nuclear-spin qubits. Experimentally, we verify the predicted Hessian-sensitive directions and demonstrate rapid convergence of the optimization protocol. The optimized gate reaches a raw fidelity of 0.9959(2), increasing to 0.99902(7) after postselection on no detected loss, and the performance is essentially unchanged under laser-power variations of up to 20%. We further show that the same fidelity Hessian directions can correct certain Hamiltonian parameter errors. These results establish low-rank Hessian optimization as an efficient and physically motivated calibration strategy for high-dimensional optimal-control gates, which is broadly applicable to many qubit types.
Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging. We propose a hybrid optimization framework that integrates optimal control theory methods with contextual deep reinforcement learning to achieve robust controlled-phase gates on two qutrits. Optimal control is first used to design high-fidelity control pulses for a nominal system model. Reinforcement learning is then employed as a calibration stage that learns small residual corrections to these pulses in the presence of static model mismatch, thereby preserving good gate performance under realistic parameter uncertainties. By learning structured, low-dimensional residual corrections conditioned on device-specific parameter variations, reinforcement learning enhances the transfer robustness of nominally optimal but parameter-sensitive control solutions across ensembles of devices. Crucially, the reinforcement learning step in our framework does not compete with the optimal control step but provides the adaptability required for realistic hardware, systematically reducing the sensitivity to parameter fluctuations. Our results establish reinforcement learning as a practical and scalable ingredient for robust calibration of quantum gates in high-dimensional systems.
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Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
Arrays of optically trapped neutral atoms are a promising architecture for the realization of quantum computers. In order to run increasingly complex algorithms, it is advantageous to demonstrate high-fidelity and flexible gates between long-lived and highly coherent qubit states. In this work, we demonstrate a universal high-fidelity gate set with individually controlled and parallel application of single-qubit gates and two-qubit gates operating on the ground-state nuclear-spin qubit in arrays of tweezer-trapped 171 Yb atoms. We utilize the long lifetime, flexible control, and high gate fidelity of our system to characterize native gates using single- and two-qubit Clifford and symmetric subspace randomized-benchmarking circuits with more than 200 controlled- Z () gates applied to one or two pairs of atoms. We measure our two-qubit entangling gate fidelity to be 99.72(3)% (99.40(3)%) with (without) postselection. In addition, we introduce a simple and optimized method for calibration of multiparameter quantum gates. These results represent important milestones toward executing complex and general quantum computation with neutral atoms.
Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we use the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope pulse parametrizations and are able to reach 99.9% controlled- Z -gate fidelity using a 64-ns-long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization, we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.